Rotational Dynamics

Notes

This note provides us an information about Moment of Inertia and Theorem of Parallel and Perpendicular Axes.
A rigid body is defined as a solid body in which the particles are compactly arranged so that the inter-particle distance is small and fixed, and their positions are not disturbed by any external forces applied on it. A rigid body can undergo both translational and rotational motion.

A rigid body is defined as a solid body in which the particles are compactly arranged so that the inter-particle distance is small and fixed, and their positions are not disturbed by any external forces applied on it.
The inertness or inability of a body to change its state of rest or uniform motion by itself is called inertia. In the case of linear motion, the mass of the object determines the inertia of the body. As the mass of the body is high the inertia is also high and hence requires more force to move it (to change the state of that body).
This note provides us an information on the moment of inertia and theorem of parallel and perpendicular axes.

This note provides us an information about radius of gyration and torque
If the body rotates in clockwise direction, then the torque applied on the body is said to be clockwise torque. On the other hand, the torque applied on a body is said to be anticlockwise torque, if it rotates the body in an anticlockwise direction .
Radius of Gyration defined as the distance from the axis of rotation to a point where the total mass of the body is supposed to be concentrated so that the moment of inertia about the axis may remain the same
The moment of inertia of a body about a given axis is equal to the torque required to produce unit angular acceleration in the body about that axis.

This note provides us an information about Angular Momentum and Principle of Conservation of Angular Momentum
1 ,Angular momentum is defined as, “ The cross product of perpendicular distance and linear momentum.
2,the magnitude of angular momentum of a body about a given axis is equal to the product of moment of inertia
3, the torque acting on a body is equal to the time rate of change of angular momentum of the body ,
4,if no external torque acts on a system, the total angular momentum of the system remains constant.

This note provides us an information about Work done by Couple, Kinetic Energy of Rotating and Rolling Body and Acceleration of Rolling Body on an Inclined Plane
1, The relational kinetic energy of a body is equal to the half the product of the moment of inertia of the body and the square of the angular velocity of the body about the given axis of rotation.
2, Two equal and opposite parallel forces acting on a rigid body at different points constitute a couple.
3, A body such as the wheel of mass m and radius R rolling along a straight line on a horizontal plane surface without slipping . When the body rolls, it rotates about the horizontal axis through the centre of mass and undergoes displacement in a forward direction. So, the body possess both rotational and translational motion.